1sir question 1 didnt get the method similiar ques here
dont know the answer
2x+y--z=28 find its positive solns
1. Find the number of solutions of the equation
x+y+z=6
the answere is 28
Please explain this in detail
2. From 5 apples, 4 mangoes and 3 bananas, in how many ways can we select atleast two fruits of each variety if
i) fruits of same species are identicle
ii) fruits of same specis are different
answere is i) 24 & ii) 1144
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6 Answers
62x+y+z= 6
you have to divide 6 into 3 parts using 2 divider...
so 8C2 = 28
622. From 5 apples, 4 mangoes and 3 bananas, in how many ways can we select atleast two fruits of each variety if
i) fruits of same species are identicle
ii) fruits of same specis are different
Case 1: Apples can be chosen in 4 ways : 2 apples/ 3 apples/ 4 / 5 apples
mangoes can be chosen in 3 ways
bananas can be chosen in 2 ways..
total number of ways is 4x3x2 = 24
Case 2: fruits of same specis are different
Number of ways to chose apples is 25 - 1- 5 = 26
Number of ways to chose mangoes is 24 - 1- 4 = 11
Number of ways to chose bananas is 23 - 1- 3 = 4
Total number of ways is 26x11x4 = 104x11 =1144
162here y+z = 28-2x
the number of solutions will be 28+1-2x if you are allowed non negative integral values values...
Now take the sum over x going from 0 to 14
3sir the qn 1 needs a correction isnt it.
but the actually ans is infinity for the qn written,as a line of x+y+z=6 in 3D have infinite points,
it will good if the qn is find the no of integral solns of the eqn x+y+z=6